Back to Course

## SS1: MATHEMATICS - 2ND TERM

0% Complete
0/0 Steps

Lesson 7, Topic 6
In Progress

# Equivalence & Bi-implication

Lesson Progress
0% Complete

#### Topic Content:

• The Converse of Statement
• Equivalent Statements

### The Converse of Statement:

Let A → B be an implication, then the converse of A → B is  B → A

### Equivalent Statements:

Let the implication X → Y be true, if Y → X is true, then X and Y are said to be equivalent statements. Thus, we write and say that X ↔ Y is a bi-implication.

### Example 7.6.1:

Given the statements:

P1: The teacher entered and started the lesson

P2: Either it will rain tomorrow or the visit will take place, or it will rain tomorrow and the visit will take place anyway.

Use appropriate symbols and truth tables to describe:

1. The conditions for P1 to be true,
2. The conditions under which P2 will be false

Solution:

1. Let the sub-statements be

A: the teacher entered

B: the teacher started the lesson

If P1 is true, then A → B is true.

Recall, the relation “and” which suggests both A and B must true before A → B could be true

Truth table

You are viewing an excerpt of this topic. Subscribe now to get full access!

Click on the button "Subscribe Now" below for Full Access

### Subscribe Now

#### Responses

error: Alert: Content selection is disabled!!